Open Access
T-overlap t-migrative functions: a generalization of migrativity in t-overlap functions
(Universidad Distrital Francisco José de Caldas (Colombia), 2020) Zapata, Hugo; Bustince Sola, Humberto; Pereira Dimuro, Graçaliz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Este artículo introduce una generalización de funciones migrativas por extensión de la condición de la operación producto aplicada en las variables. Más específicamente, en lugar de exigir multiplicar la variable x por un número real alfa; en este trabajo se trabaja este número alfa con las variables de acuerdo a una t-norma. Se denomina a esta generalización función t-migrativa con respecto a tal tnorma. Luego se analizan las propiedades principales de funciones t-migrativas en funciones t-overlap y se introducen algunos métodos de construcción de este tipo de funciones.
Open Access
Análisis de los cambios en los patrones de temperatura mediante técnicas de stream clustering
(CAEPIA, 2024) Urío Larrea, Asier; Pereira Dimuro, Graçaliz; Andreu-Pérez, Javier; Camargo, Heloisa A.; Aguirre Eraso, Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
El cambio climático afecta a las condiciones medioambientales de las distintas regiones. La capacidad de constatar estos cambios es una eficaz herramienta para adaptarse a la evolución de las condiciones. Los datos meteorológicos se generan continuamente en múltiples estaciones de todo el mundo, proporcionando una valiosa información sobre la variabilidad en el tiempo de los patrones climáticos. El estudio de este flujo de datos nos permite comprender mejor los nuevos patrones climáticos. Este trabajo explora, mediante un algoritmo de agrupamiento de flujos de datos (stream clustering), el potencial de emplear datos meteorológicos obtenidos en diferentes localizaciones geográficas para rastrear el cambio en los patrones climáticos en la Comunidad Foral de Navarra durante los últimos 20 años. El estudio de caso mostró la aplicabilidad de los métodos de flujos de datos a la segmentación incremental de regiones geográficas en función de sus factores climatológicos.
Open Access
Enhancing LSTM for sequential image classification by modifying data aggregation
(IEEE, 2021) Takáč, Zdenko; Ferrero Jaurrieta, Mikel; Horanská, Lubomíra; Krivonakova, Nada; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Recurrent Neural Networks (RNN) model sequential information and are commonly used for the analysis of time series. The most usual operation to fuse information in RNNs is the sum. In this work, we use a RNN extended type, Long Short-Term Memory (LSTM) and we use it for image classification, to which we give a sequential interpretation. Since the data used may not be independent to each other, we modify the sum operator of an LSTM unit using the n-dimensional Choquet integral, which considers possible data coalitions. We compare our methods to those based on usual aggregation functions, using the datasets Fashion-MNIST and MNIST.
Open Access
Explainable classification methods for fish species detection using hydroacoustic data
(IEEE, 2021) Costa, Lucas Tubino Bonifacio; Lucca, Giancarlo; Pereira Dimuro, Graçaliz; Borges, Eduardo N.; Emmendorfer, Leonardo R.; Weigert, Stefan Cruz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
This work aims to evaluate explainable classification methods for the detection of fish species from hydroacoustic data acquired by echo sounders at a region near the coastline of south and southeastern Brazil. Decision trees and fuzzy rule-based methods were adopted. The fitted models were evaluated by quality measures based on the performance of the classifiers and also by an expert which analyzed the usefulness of the rules on describing the schools. The models learned by the algorithms performed well for the available data and were able to represent the documented behavior of the species considered in the studied region, according to the literature.
Open Access
d-Choquet integrals: Choquet integrals based on dissimilarities
(Elsevier, 2020) Bustince Sola, Humberto; Mesiar, Radko; Fernández Fernández, Francisco Javier; Galar Idoate, Mikel; Paternain Dallo, Daniel; Altalhi, A. H.; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Takáč, Zdenko; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13
The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These functions are a generalization of the 'standard' Choquet integral obtained by replacing the difference in the definition of the usual Choquet integral by a dissimilarity function. In particular, the class of all d-Choquet integrals encompasses the class of all 'standard' Choquet integrals but the use of dissimilarities provides higher flexibility and generality. We show that some d-Choquet integrals are aggregation/pre-aggregation/averaging/functions and some of them are not. The conditions under which this happens are stated and other properties of the d-Choquet integrals are studied.
Open Access
Extensión multidimensional de la integral de Choquet discreta y su aplicación en redes neuronales recurrentes
(Universidad de Málaga, 2021) Ferrero Jaurrieta, Mikel; Rodríguez Martínez, Iosu; Pereira Dimuro, Graçaliz; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En este trabajo presentamos una definición de la integral de Choquet discreta n-dimensional, para fusionar datos vectoriales. Como aplicación, utilizamos estas nuevas integrales de Choquet discretas multidimensionales en la fusión de información secuencial en las redes neuronales recurrentes, mejorando los resultados obtenidos mediante el método de agregación tradicional.
Open Access
T-overlap functions: a generalization of bivariate overlap functions by t-norms
(Springer, 2018) Zapata, Hugo; Pereira Dimuro, Graçaliz; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
This paper introduces a generalization of overlap functions by extending one of the boundary conditions of its definition. More specifically, instead of requiring that 'the considered function is equal to zero if and only if some of the inputs is equal to zero' , we allow the range in which some t-norm is zero. We call such generalization by a t-overlap function with respect to such t-norm. Then we analyze the main properties of t-overlap function and introduce some construction methods.
Open Access
Towards interval uncertainty propagation control in bivariate aggregation processes and the introduction of width-limited interval-valued overlap functions
(Elsevier, 2021) Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Sanz Delgado, José Antonio; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Overlap functions are a class of aggregation functions that measure the overlapping degree between two values. They have been successfully applied as a fuzzy conjunction operation in several problems in which associativity is not required, such as image processing and classification. Interval-valued overlap functions were defined as an extension to express the overlapping of interval-valued data, and they have been usually applied when there is uncertainty regarding the assignment of membership degrees, as in interval-valued fuzzy rule-based classification systems. In this context, the choice of a total order for intervals can be significant, which motivated the recent developments on interval-valued aggregation functions and interval-valued overlap functions that are increasing to a given admissible order, that is, a total order that refines the usual partial order for intervals. Also, width preservation has been considered on these recent works, in an intent to avoid the uncertainty increase and guarantee the information quality, but no deeper study was made regarding the relation between the widths of the input intervals and the output interval, when applying interval-valued functions, or how one can control such uncertainty propagation based on this relation. Thus, in this paper we: (i) introduce and develop the concepts of width-limited interval-valued functions and width limiting functions, presenting a theoretical approach to analyze the relation between the widths of the input and output intervals of bivariate interval-valued functions, with special attention to interval-valued aggregation functions; (ii) introduce the concept of (a,b)-ultramodular aggregation functions, a less restrictive extension of one-dimension convexity for bivariate aggregation functions, which have an important predictable behaviour with respect to the width when extended to the interval-valued context; (iii) define width-limited interval-valued overlap functions, taking into account a function that controls the width of the output interval and a new notion of increasingness with respect to a pair of partial orders (≤1,≤2); (iv) present and compare three construction methods for these width-limited interval-valued overlap functions, considering a pair of orders (≤1,≤2), which may be admissible or not, showcasing the adaptability of our developments.
Open Access
On the normalization of interval data
(MDPI, 2020) Santiago, Regivan; Bergamaschi, Flaulles; Bustince Sola, Humberto; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; Sanz Delgado, José Antonio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
The impreciseness of numeric input data can be expressed by intervals. On the other hand, the normalization of numeric data is a usual process in many applications. How do we match the normalization with impreciseness on numeric data? A straightforward answer is that it is enough to apply a correct interval arithmetic, since the normalized exact value will be enclosed in the resulting 'normalized' interval. This paper shows that this approach is not enough since the resulting 'normalized' interval can be even wider than the input intervals. So, we propose a pair of axioms that must be satisfied by an interval arithmetic in order to be applied in the normalization of intervals. We show how some known interval arithmetics behave with respect to these axioms. The paper ends with a discussion about the current paradigm of interval computations.
Open Access
Fuzzy integrals for edge detection
(Springer, 2023) Marco Detchart, Cedric; Lucca, Giancarlo; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; López Molina, Carlos; Borges, Eduardo N.; Rincón Arango, Jaime Andrés; Julian, Vicente; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this work, we compare different families of fuzzy integrals in the context of feature aggregation for edge detection. We analyze the behaviour of the Sugeno and Choquet integral and some of its generalizations. In addition, we study the influence of the fuzzy measure over the extracted image features. For testing purposes, we follow the Bezdek Breakdown Structure for edge detection and compare the different fuzzy integrals with some classical feature aggregation methods in the literature. The results of these experiments are analyzed and discussed in detail, providing insights into the strengths and weaknesses of each approach. The overall conclusion is that the configuration of the fuzzy measure does have a paramount effect on the results by the Sugeno integral, but also that satisfactory results can be obtained by sensibly tuning such parameter. The obtained results provide valuable guidance in choosing the appropriate family of fuzzy integrals and settings for specific applications. Overall, the proposed method shows promising results for edge detection and could be applied to other image-processing tasks.